Question

В треугольнике ABC стороны AB=6 см,BC=8 см и медиана BM=5см.Найти площадь треугольника BMC.помгите пожалуйста

Answer 1

1) По th Пифагора Находим АМ

AM^2=6^2-5^2

AM^2=36-25

AM^2=11

AM=√11

2) Т.к ВМ - медиана, то: АМ=МС

S треугольника равна = √11+√11= 2√11

S тр.=1/2*2√11=√11

Ответ: √11 площадь треугольника АВС

Answer 2

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Answer 3

Problem Analysis

We are given a triangle ABC with side lengths AB = 6 cm, BC = 8 cm, and the median BM = 5 cm. We need to find the area of triangle BMC.

Solution

To find the area of triangle BMC, we need to know the length of the altitude from vertex B to side MC. Let's denote this altitude as BH.

Since BM is the median, it divides side AC into two equal parts. Therefore, AH = HC.

Let's denote the length of BH as h.

Using the Pythagorean theorem, we can find the length of AH: AH^2 = AB^2 - BH^2

Similarly, we can find the length of HC: HC^2 = BC^2 - CH^2

Since AH = HC, we can equate the two equations: AB^2 - BH^2 = BC^2 - CH^2

Simplifying the equation, we get: BH^2 - CH^2 = AB^2 - BC^2

We know that BH + CH = BM, so we can substitute BM for BH + CH: (BH + CH)(BH - CH) = AB^2 - BC^2

Simplifying further, we get: BH - CH = (AB^2 - BC^2) / (BH + CH)

Now, we have two equations: BH + CH = BM BH - CH = (AB^2 - BC^2) / (BH + CH)

We can solve these two equations simultaneously to find the values of BH and CH.

Once we have the values of BH and CH, we can find the area of triangle BMC using the formula: Area = (1/2) * BH * MC

Let's calculate the area step by step.

Calculation

Given: AB = 6 cm BC = 8 cm BM = 5 cm

Using the equation BH + CH = BM, we can substitute the values: BH + CH = 5 cm

Using the equation BH - CH = (AB^2 - BC^2) / (BH + CH), we can substitute the values: BH - CH = (6^2 - 8^2) / (5)

Simplifying the equation, we get: BH - CH = (-20) / 5 BH - CH = -4

Adding the two equations BH + CH = 5 and BH - CH = -4, we get: 2BH = 1 BH = 1/2 cm

Substituting the value of BH in the equation BH + CH = 5, we get: 1/2 + CH = 5 CH = 9/2 cm

Now, we have the values of BH = 1/2 cm and CH = 9/2 cm.

Using the formula for the area of triangle BMC, we can calculate the area: Area = (1/2) * BH * MC Area = (1/2) * (1/2 cm) * (5 cm) Area = 5/4 cm^2

Therefore, the area of triangle BMC is 5/4 cm^2.

Answer

The area of triangle BMC is 5/4 cm^2.